Friday, January 13, 2006

Friday Stats of Questionable Value

I've gone off on a bit of a tangent with the stat-crunching I did Monday, trying to get a better sense of the importance of special teams. I'm going to try to walk through some numbers here that aren't overly complicated, but trying to grasp their meaning does make my head hurt a bit.

First, we have even strength scoring. The average ES GAA amongst the 30 NHL teams is about 2.65. Obviously, the average Goals For Average (GFA) is also 2.65, and the average ES Goal Differential (GD) is 0.00; since every ES goal that one team scores is given up by another.

Second, the average SH GAA (or PP GFA, same diff) is about 6.75. So the difference between the average team's likelihood of surrendering a goal while SH, compared to ES, is about 4.10 (6.75-2.65). This is basically the measure of PP scoring.

Third, the average PP GAA (or SH GFA) is about 0.70. So the difference between the average team's likelihood of surrendering a goal while on the PP, compared to ES, is about -1.95 (0.70-2.65). This is basically the measure of SH scoring.

These second and third items, when combined, are the average Goal Differential on special teams: 4.10 minus (-1.95) = 6.05. Meaning: the theoretical exactly average team, which would expect to tie every game if it were played all at ES, would win every game by 6 goals if they played them all on the PP.

(The other (only?) slightly interesting aspect of this stat is the breakdown of Why the PP is Good: roughly two-thirds of the reason is the increased chance of scoring a goal, and one-third is the reduced likelihood of allowing one.)

Now of course, no team is exactly average, so when you break this stuff down by team, there are some interesting outlying numbers. Let's look at the best and worst teams in each "category", plus the Flames and Oilers numbers.

Difference between ES GAA and SH GAA:

Average: 4.10

Smallest: Minnesota: 1.58

Biggest: Atlanta: 5.73

Flames: 5.47

Oilers: 4.01

Minnesota has a fantastic PK relative to their decent ES numbers. Atlanta has an atrocious PK, so even though their ES numbers are kind of crappy, they have the biggest difference. The Oilers are average in both categories, so their difference is also average. The Flames have a great ES GAA but below average PK, so their difference is quite large (3rd worst in NHL).

In short, going on the PK hurts Minnesota's ability to prevent goals the least, and Atlanta's the most. It also hurts Calgary more than everyone but Atlanta and Washington.

Difference between ES GFA and SH GFA:

Average: 1.95

Smallest: Toronto: 0.97

Biggest: Rangers: 2.61

Flames: 1.67

Oilers: 1.62

Toronto has a below average ES GFA, but scores lots of shorthanded goals. Rangers have an above average ES GFA, and have scored only one SH goal all year. In short, going on the PK hurts Toronto's scoring the least, and the Rangers' scoring the most.

Now, combining those two categories, you get this:

Difference between ES GD and SH GD:

Average: 6.05

Smallest: Minnesota: 3.24

Biggest: Atlanta: 7.64

Flames: 7.14

Oilers: 5.64

Translation: taking a penalty is least harmful to Minnesota, since it has the least impact on their ability to score and prevent goals. It's most harmful to Atlanta. It's very harmful to Calgary, mainly because (in relative terms) their PK is so bad relative to their regular ES play. It's slightly less harmful than the average to Edmonton.

Now you can do the whole thing again for teams' PP (and I did).

Difference between PP GFA and ES GFA:

Average: 4.10

Biggest: Detroit: 6.54

Smallest: Tampa Bay: 2.21

Flames: 4.36

Oilers: 4.56

Difference between PP GAA and ES GAA:

Average: 1.95

Biggest: St. Louis: 3.14

Smallest: Ottawa: 1.18

Flames: 1.82

Oilers: 2.41

Difference between PP GD and ES GD:

Average: 6.05

Biggest: Detroit: 8.20

Smallest: Tampa Bay: 4.07

Flames: 6.18

Oilers: 6.97

Translation: going on the PP helps Detroit more than any other team, mainly because their PP scoring % is that damn good. Tampa has nearly the worst PP in the league somehow, so relative to their average scoring at ES, going on the PP helps them the least. Ottawa has an excellent ES GAA but allows an average # of SH goals, so going on the PP helps them prevent goals less than any other team. St. Louise has an awful ES GAA, but doesn't allow many SH goals, so going on the PP helps them prevent goals more than any other team.

Sub-Conclusion: the value (such as it is) of all these numbers is predictive. If Detroit is getting a lot of power plays, they're going to win. If Atlanta (or Calgary) is taking a lot of penalties, they're going to lose, etc. etc.

However, you can also use them to look backwards, and see which teams are getting killed by taking penalties, and which ones are gaining an advantage by drawing them.

The figures are available for how much time each team spends on the PP and SH, and it's relatively simple to correct for PP/PK success and assess whether those times are above or below average. I'm going to call this Discipline, although that's overly simplistic: factors besides discipline could include hard work, luck, and reputation; even referee favoritism if you believe in that.

To illustrate what I'm talking about, take Ottawa (please!). The Sens have scored 57 PPG and allowed only 42; they've scored 12 SHG and allowed only 4. Obviously there's nothing to complain about with their special teams. However, even after correcting for how good they are at it (and thus spend a bit more time on the PK and less on the PP than if they were average), they spend 16 seconds per game less than the average on the PP, and 36 seconds more than the average on the PK.

Correspondingly, this hurts the Sens. They're down 2.7 goals relative to if they took an average amount of penalties, and they're also down 2.5 goals relative to if they drew an average amount of penalties. This total of 5.3 goals, as Mr. Poisson could tell you, fairly reliably corresponds to a loss of 2 points in the standings (2.8 goals = 1 point).

Here's the teams whose "Discipline" has cost them the most goals:

FLA -10

CHI -8

OTT -5

WSH -5

CBJ -5

Except Ottawa, this makes quite a bit of sense: bad teams, undisciplined, bad special teams, the whole deal. The crew with the best discipline, however, is a bit more of a surprise:

CAR +10

TBL +9

NJD +9

SJS +7

LAK +7

There you have it. One last stat that stood out to me: how good is the Wild PK, and how bad are the Blues? The Blues ES GAA is 3.58, and the Wild SH GAA is 4.03. Basically, it's almost as easy to score on St. Louis even-strength as it is to put a PP goal past Minnesota.

I'm not sure I follow your Ottawa example. Obviously one of the reasons the Sens have less PP time than average is because they score so much on them (i.e., proportionately fewer powerplays go a full two minutes). I assume you took this into account when you say you "corrected" the numbers, although it isn't clear to me what exactly this correcting consisted of (pp mins/pp goals?).

Even so, this might be a case where looking at PP time (even when corrected) rather than number of penalties drawn might be misleading. For example, what does 16 seconds/game of pp time actually mean? How many actual penalties does Ottawa draw in comparison to other teams? Is it at all realistic to think that they should be able to draw more penalties? How many more penalties a game would be required to make up that 16 seconds/game?

And finally, do these numbers include 4 on 4 play? If we are going to talk "discipline" and drawing penalties, there must be teams out there, and I bet Ottawa is one of them, where 4 on 4 success is much better than 5 on 5 success. I.e., drawing an offsetting penalty is almost as good as drawing a pp.

Second: the corrections for PP/PK success & failure I did the best way I could figure. I gave Ottawa one extra minute of PP time on their season total for every PPG they scored above the league average. Same with the other above-average PP teams. I deducted one minute of PP time for every PPG below the league average as well, for the below-average PP teams.

Same entire deal with the PK.

The penalty numbers (e.g. # of minors) aren't available by team at NHL.com; you have to root through stats for each team. Plus, my way might be better, since mine accounts for offsetting penalties and Peca Specials (taking a penalty while on the PP).

Is it at all realistic to think that they should be able to draw more penalties? Maybe not. Or maybe they can skate harder, or sell out in the corners more, or dive better. I don't know.

4-on-4 play is lumped in with 5-on-5 for now, in the absence of data on 4-on-4 time. Point taken that some teams are better 4-on-4 than 5-on-5 (although Ottawa is fantastic 5-on-5; I doubt that they're one of them). However, there's no way that there's any team for whom 4-on-4 is almost as good as a PP.

Lastly re: "what does 16s/gm actually mean?" - I don't really know, although that's what I was trying to poke at. The best way I can answer it is to multiply that 16s by how many games the Sens have played, and then look at how that time affected their ability to score and prevent goals. It hurt it, by about 2.5, best I can tell.

All that said: the bottom corner of my spreadsheet was column AC, row 174. That's a lot of math, and I may well have mucked some of it up.

Right, I didn't mean to suggest that Ottawa couldn't draw more penalties. I just didn't know where they were already in terms of number of penalties taken/drawn per game relative to other teams. I could look it up, but I'm lazy.

Also, call be a statistical skeptic, but given that the one minute added and subtracted for pk and pp goals is pretty rounded/generalized/arbitrary, I'm having a tough time believing that 16 seconds below average means anything at all.

In other words, I'm not yet convinced that all this mathemagic show us anything more than we already knew -- i.e., teams with good powerplays benefit from getting lots of opportunities more than teams with bad powerplays, and teams with good penalty kills don't get burned as often as teams with bad penalty kills.